Depends on what you’re doing, platform, goals, etc. If you’re required to use a department or other “pool” rifle, then sure, train around whatever configuration that is. If for some make believe scenario, you think you’ll be doing field pick-ups on rifles, then I guess training on a non-ambi platform makes sense.
Disclaimer, I’m right handed, and right eye dominant, but I’m relatively ambidextrous on shooting rifles, and considered switching to shooting left-handed.
I personally want to maximize the performance on my ARs, whether that’s shooting matches, drills, classes, or work applications, so anything that will improve that with no real downsides, I’d take. I don’t want to leave capabilities on the table. I don’t buy into the likelihood of a battle-field pickup, and if that were to happen, I’ve trained enough on stock platforms that I’d be functional.
For ARs, if I was left handed, I would use a standard quality gun, BCM, SOLGW, etc and get a reversed safety or at least an ambi one with a lo-profile lever on the off side (I don’t like ambi’s…), a left handed mag release from FCD, the FCD rear-biased bolt catch, a good ambi-charging handle (BCM, Radian, Geisselle, etc) and the FCD low-drag forward assist. Another aspect I’m told is important, is good gassing on the rifle, and if you’re running a can, a flow-through design would probably be nice so you don’t eat as much gas.
The rest of things, like furniture, slings, etc just swap from your right handed setup.
Anything rifle outside of ARs, isn’t my forte, so I’d defer to what others said. Gear setup shouldn’t be too bad, lots of dudes shoot rifle and pistol opposite. Blowers runs his rifle mag in front of his pistol, most guys I work with put their rifle mag behind their pistol though.